Finite Group DatabasebetaFinite Group Databasebeta| order | 31311 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C49 · Schur multiplier (H2) = C3 |
| direct product | C32×C71⋊C49 |
| unambiguous semidirect product | C71⋊(C32×C49) |
| unambiguous semidirect product | (C3×C71)⋊(C3×C49) |
| unambiguous semidirect product | (C32×C71)⋊C49 |
| derived, Sylow | C71 ⋊ C32×C49 |
| Hall | C32×C71 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C7 | C71⋊C7 |
| commutator, hypocenter | C71 | C32×C49 |
| Frattini | C7 | C32×C71⋊C7 |
| Fitting, socle, prime radical | C32×C7×C71 | C7 |
| cosocle | C7×C71 | C32×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C32×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31311 |
1071 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31311, 5);